STRUCTURAL DESIGN OF A LIGHT STEEL FRAME HOUSE
PEDRO EDUARDO RODRIGUES MENDES
Dissertação submetida para satisfação parcial dos requisitos do grau de
MESTRE EM ENGENHARIA CIVIL — ESPECIALIZAÇÃO EM ESTRUTURAS
Orientador: Professor Doutor José Miguel de Freitas Castro
Coorientador: Doutor Smail Kechidi
OUTOBRO DE 2019
MESTRADO INTEGRADO EM ENGENHARIA CIVIL 2018/2019
DEPARTAMENTO DE ENGENHARIA CIVIL Tel. +351-22-508 1901 Fax +351-22-508 1446 [email protected]
Editado por
FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO Rua Dr. Roberto Frias 4200-465 PORTO Portugal Tel. +351-22-508 1400 Fax +351-22-508 1440 [email protected] http://www.fe.up.pt
Reproduções parciais deste documento serão autorizadas na condição que seja mencionado o Autor e feita referência a Mestrado Integrado em Engenharia Civil - 2018/2019 - Departamento de Engenharia Civil, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal, 2019.
As opiniões e informações incluídas neste documento representam unicamente o ponto de vista do respetivo Autor, não podendo o Editor aceitar qualquer responsabilidade legal ou outra em relação a erros ou omissões que possam existir.
Este documento foi produzido a partir de versão eletrónica fornecida pelo respetivo Autor.
Structural Design of a Light Steel Frame Dwelling
Aos meus Pais
Structural Design of a Light Steel Frame Dwelling
Agradecimentos
O trabalho que se segue representa o culminar de um longo percurso percorrido pelo autor, ao longo do qual este contou com a ajuda de diversas pessoas que merecem o seu agradecimento. Em primeiro lugar um obrigado a todos os professores que me instruíram em todo o meu percurso académico, e em especial ao meu orientador Professor Doutor José Miguel Castro pela forma forma como cedo se disponibilizou para me ajudar a conhecer mais este assunto, e pela confiança que transmitia a cada obstáculo encontrado. Do mesmo modo, não posso de deixar de agradecer ao meu coorientador Dr. Smail Kechidi, cujo conhecimento sobre o assunto é notório e sem quem teria sido impossível fazer um trabalho tão completo uma vez que esteve sempre disponível para esclarecer todas duvidas que me foram surgindo. Aos meus colegas e amigos que me acompanharam nos bons e maus momentos ao longo destes anos, por todo o apoio que me deram quer esclarecendo-me dúvidas quer dando apoio moral quando assim o precisava. E principalmente, à minha família, por todos os sacrifícios que fez para que eu pudesse ter um curso superior, pelo apoio incondicional que me deram, tendo sempre confiado em mim.
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Resumo
Nos últimos anos surgiram novos sistemas de construção que garantem alto desempenho estrutural e ambiental. Entre outros, a estrutura de aço leve (LSF) está se tornando um sistema estrutural eficaz para edifícios de baixo e médio porte. Várias vantagens, como alta relação resistência / peso, baixo custo de transporte e facilidade de construção, agilizam o uso de elementos de aço enformado a frio em muitos países quer como elementos estruturais quer não estruturais. Além de oferecer excelentes propriedades estruturais, térmicas e acústicas, este sistema apresenta ainda uma solução sustentável, uma vez que a estrutura de aço é 100% reciclável e, ao mesmo tempo, permite economias significativas em termos de energia. Esta dissertação concentra-se nas propriedades das construções LSF, passando pelas várias características inerentes a este método, como as propriedades dos materiais e as principais seções transversais utilizadas, além de apresentar alguns revestimentos disponíveis no mercado. Posteriormente, é apresentado um estado de dimensionamento de acordo com as práticas europeias de projeto de uma estrutura de dois andares, feita de aço leve, adotando paredes resistentes ao corte com revestimento de madeira OSB como sistema de resistência lateral à carga.
Palavras-chave: LSF, estruturas de aço leve, aço enformado a frio, dimensionamento de estruturas, Eurocódigos, sustentabilidade.
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Abstract
In recent years, new innovative systems to ensure high structural and environmental performance have emerged. Among others, light steel framing (LSF) is becoming an effective structural system for low- and mid-rise buildings. Several desirable features, like high strength-to-weight ratio, low shipping cost and easiness of construction, expedite the use of CFS members in many countries as both structural and nonstructural members. While providing excellent structural, thermal and acoustic properties, this method also offers a sustainable solution, since the steel frame is 100% recyclable and at the same time, enables significant savings in terms of energy. This dissertation focusses on the properties of LSF constructions, going through the various characteristics inherent to this method like the properties of materials and main cross-sections used, while also presenting some claddings available in the market. Subsequently, analysis and design according the European design practices of a 2-storey structure made of light steel frame adopting OSB wood-sheathed shear walls as lateral load resisting system, are carried out. Key words: Light steel frame, structural design, Eurocodes, sustainability.
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Table of Contents
Agradecimentos ...... i Resumo ...... iii Abstract ...... v
1. Introduction ...... 1
Contextualization ...... 1 Scope and objectives ...... 2 Dissertation layout ...... 2
2. Historic contextualization ...... 5
3. Materials ...... 7
Steel ...... 7 3.1.1. Protection ...... 8 3.1.2. Fabrication process ...... 8 3.1.3. Common cross-sections ...... 11 Insulation and claddings ...... 13 3.2.1. Facade claddings ...... 13 3.2.1.1. Structural claddings ...... 13 3.2.1.2. Non-structural claddings ...... 16 3.2.2. Thermal insulation ...... 18 3.2.3. Acoustic insulation ...... 19 Connections ...... 19 3.3.1. Steel-to-steel connections ...... 19 3.3.2. Cladding to framing connections ...... 20
4. Constructive Method ...... 21
Terminology ...... 21 Foundations ...... 23
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Constructive methods ...... 24 4.3.1. Stick construction ...... 24 4.3.2. Panel construction ...... 25 4.3.3. Modular construction ...... 26 4.3.4. Balloon frame construction ...... 27 Bracings ...... 27 4.4.1. K - Bracings ...... 28 4.4.2. X - Bracings ...... 28 4.4.3. Diaphragm Effect ...... 29
5. Design regulations ...... 31
Cold-formed steel specific phenomenon ...... 31 5.1.1. Local buckling ...... 31 5.1.2. Torsion ...... 31 5.1.3. Distortion ...... 32 Cross-section classifications ...... 32 Effective properties ...... 34 Resistance of cross-sections ...... 34 5.4.1. Axial tension ...... 35 5.4.2. Axial compression ...... 35 5.4.3. Bending moment ...... 35 5.4.4. Shear force ...... 36 5.4.5. Torsional moment ...... 37 5.4.6. Local transverse forces ...... 37 5.4.7. Combined tension and bending ...... 39 5.4.8. Combined compression and bending ...... 39 5.4.9. Combined shear force, axial force and bending moment...... 39 5.4.10. Combined bending moment and local load or support reaction ...... 40 Buckling Resistance ...... 40 5.5.1.Uniformly comprised elements ...... 40 5.5.1. General ...... 40 5.5.2. Flexural buckling ...... 40 5.5.3. Torsional buckling and torsional-flexural buckling ...... 41 5.5.4. Lateral-torsional buckling of members subjected to bending ...... 43 5.5.5. Bending and Axial Loading ...... 43 Serviceability limit state ...... 44 5.6.1. General ...... 44
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5.6.2. Vertical deflections ...... 44 5.6.3. Horizontal displacements ...... 45 Dynamic Effects/ Vibrations ...... 46 Wall Diaphragms ...... 46
6. Case Study ...... 49
Case study overview ...... 49 6.1.1. Architeture ...... 49 6.1.2. Exterior walls ...... 51 6.1.3. Interior walls ...... 51 6.1.4. Floor slab...... 52 6.1.5. Roof slab ...... 53 Regulatory requirements ...... 53 Loads ...... 53 6.3.1. Self-weight...... 53 6.3.2. Dead Loads ...... 54 6.3.3. Live Loads ...... 55 6.3.4. Wind Loads ...... 56 6.3.5. Second order effects ...... 59 Modeling ...... 60 6.4.1. General ...... 60 6.4.2. Modeling the bracings ...... 61 6.4.3. Modal analysis ...... 62
7. Design checks ...... 65
Vertical Elements ...... 65 7.1.1. Second floor exterior walls ...... 65 7.1.2. Second floor interior walls ...... 66 7.1.3. First floor exterior walls ...... 67 7.1.4. First floor interior walls ...... 69 Horizontal Elements ...... 69 7.2.1. First floor main beam ...... 71 7.2.2. First floor corner beams ...... 74 7.2.3. First floor joists ...... 77 7.2.4. Rooftop beams ...... 80 7.2.5. Garage roof ...... 81 Bracings ...... 83
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8. Conclusions ...... 85
Developed work ...... 85 Future Work ...... 85
Bibliography ...... 87
9. Annex ...... 91 Effective Cross-sections Properties ...... 92
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Tables of figures
Figure 1-1 - LSF prefabricated dwelling [1] ...... 2 Figure 2-1 - Percentage of the use of steel structures in habitation buildings[21] ...... 6 Figure 3-1 - Effect of cold forming in the mechanic properties of a U-profile [6] ...... 8 Figure 3-2 - Press braking process [21] ...... 9 Figure 3-3 - Rolling process [8] ...... 10 Figure 3-4 - Cold forming a closed cross-section process [8] ...... 11 Figure 3-5 - Most common cross-sections shapes [21] ...... 11 Figure 3-6 - Front-to-front and back-to-back built-up cross-sections [18] ...... 12 Figure 3-7 - Evolution of the critical tension with the increase of stiffeners [22] ...... 12 Figure 3-8 – CLT board [30] ...... 14 Figure 3-9 - OSB boards [31] ...... 14 Figure 3-10 - "Viroc" boards [11] ...... 16 Figure 3-11 – Different kind of gypsum boards [12] ...... 17 Figure 3-12 - Scheme of Isolpro boards application on a LSF floor [4] ...... 18 Figure 3-13 - Types of screws heads [32] ...... 20 Figure 4-1 - Scheme of track to foundation connection [19] ...... 23 Figure 4-2 - Stick construction [19] ...... 25 Figure 4-3 - Panel construction [19] ...... 26 Figure 4-4 - Modular construction [19] ...... 26 Figure 4-5 - Platform construction (on the left) and balloon frame construction (on the right) [18] .. 27 Figure 4-6 - K-Bracings [18] ...... 28 Figure 4-7 - X-Bracings [18] ...... 29 Figure 5-1 Effective cross-section under compression [4] ...... 35 Figure 5-2 - Effective cross-section for bending resistance to bending moments [4] ...... 36 Figure 5-3 - Longitudinally stiffened web [4] ...... 37 Figure 5-4 - Examples of cross-sections with a single web [4] ...... 38 Figure 5-5 - Examples of cross-sections with two or more webs [4] ...... 39 Figure 5-6 - Schemes of torsional buckling( at the left) and flexural-torsional buckling (at the right) . 41 Figure 5-7 - Example of point-symmetric cross-section [4] ...... 42 Figure 5-8 - Mono-symmetric cross-sections susceptible to torsional-flexural buckling [4] ...... 42 Figure 5-9 - Definitions of vertical deflections [22] ...... 44 Figure 5-10 - Definition of horizontal displacements [22] ...... 45 Figure 5-11 - Forces acting on: a) wall panel b) framing c)sheet [33] ...... 46 Figure 5-12 - Nominal shear resistance per unit length for seismic and other in-plane loads, for shear walls sheathed with wood structural panels on one side of the wall [17] ...... 47 Figure 6-1 - Facade of the dwellings [34] ...... 49 Figure 6-2 - 2nd floor plan views [34] ...... 50 Figure 6-3 - 1st floor plan views [34] ...... 50 Figure 6-4 - Side View [34] ...... 51 Figure 6-5 - Exterior walls scheme [35] ...... 51 Figure 6-6 - Interior walls scheme [35] ...... 52 Figure 6-7 - Floor slab scheme [35] ...... 52 Figure 6-8 - Scheme of simplification model [35] ...... 57 Figure 6-9 - Top view with wind directions [35]...... 58
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Figure 6-10 - Wind pressure X+ direction [26] ...... 58 Figure 6-11 - Representation of Horne method [21]...... 59 Figure 6-12 - Typical state-of-the-practice shear wall model [24] ...... 62 Figure 6-13 - First mode of vibration [26] ...... 63 Figure 7-1 - Final configuration of floor slab [26] ...... 70 Figure 7-2 - Final configuration of rooftop slab [26] ...... 70 Figure 7-3 - Garage roof slab configuration [26] ...... 71 Figure 7-4 - Main beam maximum shear force [26] ...... 71 Figure 7-5 - Main beam cross-section and section properties [26]...... 72 Figure 7-6 - Main beam maximum deflection [26] ...... 74 Figure 7-7 -First floor corner beams [26] ...... 74 Figure 7-8 - Deflection of the corner beam without support [26] ...... 75 Figure 7-9 - C170 Back-to-back cross-section [26] ...... 76 Figure 7-10 - Corner beam deflection with column support [26] ...... 77 Figure 7-11 - First floor joists [26] ...... 77 Figure 7-12 - Generic bridging and blocking details [19] ...... 78 Figure 7-13 - First floor joists deflections [26] ...... 79 Figure 7-14 - Hat-section [26] ...... 80 Figure 7-15 - Worst rooftop beam bending moments diagram [26] ...... 81 Figure 7-16 - Garage beams deflection [26] ...... 83
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Table of charts
Table 3-1 - Requirements specified in NP EN 300 to consider a OSB board as structural element [6] 13 Table 4-1 - Main terms used in LSF construction [16]...... 21 Table 5-1 Maximum width-to-thickness ratios for compression parts [21] ...... 33 Table 5-2 - Maximum width-to-thickness ratios for compression parts [21] ...... 34
Table 5-3 - Shear buckling strength fbv [4] ...... 36 Table 5-4 - Recommended values for the limits of vertical deflections [21] ...... 45 Table 6-1 - Weight per meter of most common cross-sections [2] ...... 54 Table 6-2 – Resume of considered dead loads [23] ...... 54 Table 6-3 - Resume of considered live loads ...... 55 Table 6-4 - Calculation of the critical factor value ...... 60 Table 7-1 - Second floor exterior studs stresses [26] ...... 66 Table 7-2 - Second floor exterior studs safety checks ...... 66 Table 7-3 - Second floor interior studs’ stresses [26] ...... 67 Table 7-4 - Second floor interior studs safety verifications ...... 67 Table 7-5 - C170 studs resistant properties according to number of profiles ...... 68 Table 7-6 - Triple section safety verifications ...... 68 Table 7-7 - C90 studs resistant properties ...... 69 Table 7-8 - Stresses on the main beam [26] ...... 72 Table 7-9 - Main beam cross-section properties ...... 72 Table 7-10 - Main beam resistant properties...... 73 Table 7-11 - Main beam safety checks ...... 73 Table 7-12 - Stresses on corner beam [26] ...... 75 Table 7-13 - Corner beam, cross-section properties ...... 76 Table 7-14 - Corner beam resistant properties ...... 76 Table 7-15 - Corner beam safety checks ...... 76 Table 7-16 - Stresses on most solicited joist [26] ...... 78 Table 7-17 - First floor joists safety checks ...... 79 Table 7-18 - Hat section properties ...... 80 Table 7-19 - Hat-section beam resistant properties ...... 80 Table 7-20 - Stresses on the most solicited rooftop beam [26] ...... 80 Table 7-21 - Rooftop beam safety checks ...... 81 Table 7-22 - Garage roof beams stresses ...... 82 Table 7-23 - Garage beams cross-section properties ...... 82 Table 7-24 – Garage beams resistant properties ...... 82 Table 7-25 - Rooftop beam safety checks ...... 82
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Table of acronyms
CEN – Comité Européen de Normalisation CLT – Cross Laminated Timber EC0 – Eurocode 0 EC1 – Eurocode 1 EC3 – Eurocode 3 EC5 – Eurocode 5 EC8 – Eurocode 8 LSF – Light Steel Frame HVAC – Heating, Ventilation and Air Conditioning HSHW – Health Safety and Hygiene at Work OSB – Oriented Strand Boards USA – United States of America
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Introduction
Contextualization
Having a home or even just a roof is not only a desire, but also a concern for many people around the world. Faced with this need, the construction industry has sought to adopt innovative technologies and construction methods that allow the reduction of costs, time and simultaneously guarantee the quality required by customers. Currently, the execution of the structure of buildings is based on the use of reinforced concrete, stone masonry, steel profiles or even wood. One solution that has been growing in recent years is the light steel construction, commonly known as LSF - Light Steel Frame, due to its constructive system that allows the construction of buildings that present, in terms of safety and comfort, a high quality homes using the latest precision engineering technology. Instead of a more traditional approach, which consists of the use of concrete and brick, the structure of a house will consist of resistant walls composed of several metal profiles in galvanized steel of small thickness and covered by several types of sheathings. It should be noted at the outset that the key word in this concept is Light, since it is its main characteristic and from here advent all its advantages. Because of this lightness, each element is easy to transport, handle, and assemble, reducing the time of construction, and the equipment needed. Furthermore, since steel is mostly priced by the weight, light elements will be cheaper. Due to the fact that these metal profiles have a cross-sectional thickness between 0.9 and 3.2 mm, combining the material high strength and a considerable lightness, a better structural performance is obtained [1]. On top of being used worldwide for new construction, the low weight of steel and other materials used, make the LSF constructive method ideal for remodeling old buildings. The use of lightweight materials reduces transportation and lifting difficulties while at the same time eliminating the need to reinforce the old building structure, since it the increased load won’t be relevant. In some cases, this advantage makes LSF the only possible alternative for splitting spaces, adding a new floor or replacing wood floors or already degraded roofs. Another great advantage of this constructive method is the prefabrication by modules, and the walls can be assembled in a factory then exported and assembled in a short time in the desired place. An example of success is the 650 m2 dwelling shown in Figure 1-1, prefabricated in China and assembled in Melbourne (Australia), and it took only sixty days for the fabrication and three weeks for the assembly, for a total of one hundred days of construction [1]. Note that, in traditional construction this would have needed about one year to be built.
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Figure 1-1 - LSF prefabricated dwelling [1]
On the other hand, sustainable development is a key challenge in our society and light steel construction offers the guarantee of not harming the environment. In addition to being 100% recyclable, the use of steel in a building reduces drastically the usual debris. Finally, it also allows significant energy savings, both in its construction and in its use [2]. For all these advantages, and because the author considers the LSF as the future of building construction, this dissertation was elaborated.
Scope and objectives
The main purpose of the dissertation is to acquire knowledge about a constructive method in clear expansion, identifying its current uses and realizing its potentialities and limitations. In this way, two different branches are identified, which will be dealt with herein, the design features and the normative regulations of light steel structures. On the side of the conception of LSF, to understand how the construction process works, what are the dimensions and shapes of the metallic profiles, what are the thermal and acoustic insulation, and the coating materials, and how the different elements are assembled. On the structural design side, what are the specific characteristics of light-gauge steel, how important are the different structural elements, and what requirements must be met in the applicable standards.
Dissertation layout
This dissertation is divided into 8 chapters. As the title seems to suggest, “Structural Design of an Light Steel Frame Dwelling”, this manuscript implies the knowledge about the behavior, constructive method and design implications of light steel framing buildings, as well as the main properties of light steel sections, in order to be applied to a real case study. The second chapter is a brief introduction and contextualization to light steel framing structures, how this constructive method has appeared and how it has been developed giving a small historic backward. As well, the main advantages and disadvantages of this system are highlighted. In the third chapter, an intensive presentation is made about all the materials involved in the structural behavior of an LSF structure. All the properties used in the framing system, including the mechanical
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and chemical properties of the steel, the coating properties, the most common cross-section shapes as well as their inherent properties and how they were obtained. In addition, some of the possible claddings are presented, since as it will be explained more ahead, they are part of the structure. The main advantages and disadvantages of each one are explained so that it would be possible to know what innovative solutions exist in the market nowadays. Subsequently, the possible connections to assemble all the structural elements together are presented, describing how they should be used and how the most common cases to each one should be applied. The fourth chapter is about the constructive method, where it is introduced some specific terminology of this kind of construction, and it is explained in detail how this type of construction is made. The fifth chapter is about the reglementary norms, where all the ultimate and serviceability requirements are identified and explained, as well as some phenomena related to light-gauge steel members. Chapter six is about the case study, where a brief presentation of the building, location and specifying some of its main characteristics, is made. Additionally, the applied loads are identified and calculated according to the European standard (Eurocode 1) [3]. In the seventh chapter, the obtained results are explained and analyzed according to Eurocode (EC3) [4] and it is presented the final designs. Lastly, in chapter eight, a reflection is made about the results obtained and some suggestions about future works.
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Historic contextualization
To define the historical background of the LSF we must go back to the United States in the nineteenth century. In those years, the population of the country multiplied by ten being necessary to resort to the materials available locally and practical and fast methods that allowed to increase the productivity in the construction of new houses. This type of constructive system with wood structure is usually called wood framing. Wood was then used as the main structural element of residential buildings and thus remained until today. By the end of World War II, steel was an abundant resource and metallurgical companies had gained considerable experience in using metal because of the war effort. First used in the partitions of large buildings with iron structure, light steel shaped or cold formed was used in partitions of dwelling buildings and believed that it could totally replace the wooden structures in the houses. Applications of cold-formed steel are found as early as the year 1850, both in the US and in Britain. However, the US legislation applicable to the LSF only began to take its first steps in the 1940s. Another major push came in the 1980s when several forests were closed to the timber industry. This has led to the decline in the quality of wood used in construction and to large fluctuations in the price of this raw material. In 1991, the price of wood used in construction rose significantly in a few months, which led many manufacturers to switch to steel immediately. According to the Steel Recycling Institute, to build a wooden dwelling with about 186 m2 would be needed between 40 to 50 trees, however, building that same steel housing would require only 6 scrapped cars. [5] After this explosive but unstructured start, associations of technicians and builders were created and the LSF started to be seen professionally. Today it is incomparably easier to work light steel than fifteen years ago. The system is in full development and is widely used in the construction of buildings in the most developed countries, such as the USA, Japan, Australia New Zealand, United Kingdom, Northern Europe and South Africa. The Figure 2-1 shows the percentage of steel habitations in these different countries.
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Figure 2-1 - Percentage of the use of steel structures in habitation buildings[21]
In Portugal, although with less impact than in the countries listed above, there was also the same tendency to seek alternatives to traditional construction processes. Since the initial faltering of the LSF in Portugal around 1993, the demand for houses with steel structure has been increasing, so as to find quality solutions at competitive prices. [6]
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Materials
The correct choice of materials can contribute a lot to the value of a property, not only in terms of finishes, but mainly nonvisible elements such as structural elements as well as thermal or acoustic insulation. In the design of buildings in LSF this selection has an even greater relevance since it is necessary to consider the nature of the materials, considering the compatibility between them, and with the different specialties. Therefore, it is extremely important that there is good communication between the different specialties’ technicians and the structural designer, which must master many aspects of civil construction. Finally, it should be emphasized that beyond the optimization of the choice of materials, it is also very important that the manpower has enough knowledge about this method so that the final product has the best quality possible.
Steel
By far the largest producer and exporter of steel in the world is China [7]. Here the raw materials of new or recycled mineral are transformed into galvanized steel sheets of thicknesses that can vary between 0,9mm and 3,2mm and with necessary widths to form the profiles and length of several hundred meters rolled in reels. This steel reels have the following characteristics:
2 Yield strain (fy) in the range of 220-460 N / mm (however, it is now possible to use high strength steels - up to 600 N / mm2),
2 Ultimate strain (fu) in the range 300-720 N / mm ;
The relation between the ultimate strain and the yield strain (fu / fy) with values in the range of 1.1-1.9; The maximum extension in the range 14-25% However, these values are not the same after bending, since the cold folding operation increases the yield stress of the steel (fy) to a modified yield stress (fya), also raising its ultimate strength (fu) and reducing its ductility.
The value of fya depends very much on several parameters such as the kind of steel, the kind of stress (compression or tension), relation between fu / fy, the relationship between the bend radius and the thickness (ri / t), the amount of cold work performed, and is estimated in different ways in several standards.
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As the main zones affected by the cold forming process are the corners, these will have mechanical properties different from the flat zones. Figure 3-1 illustrates the variation of the mechanical properties along the cross-section of a U-profile.
Figure 3-1 - Effect of cold forming in the mechanic properties of a U-profile [6]
In this particular case, the corner region has an increase of 28% for fu and 70% for fy, and hence the mean yield strength of the section fya can in certain cases be used in substitution of fy. Even if the designer chooses the more conservative option and does not use fya, he should be aware of this increase of the yield stress. [8]
3.1.1. Protection
Galvanizing is the treatment that not only protects steel from rust and corrosion, but also gives it a bright and attractive appearance is guaranteed through a molten zinc bath ensuring a surface coating with a density that can range from 30g / mm2 to 600g / mm2. Thanks to this type of protection, it is possible for the steel to remain in service for about 40 years without maintenance and can be freely folded, painted and welded. However, it has the disadvantage that it cannot be used under the ground without being properly covered. [9] Also, if weld is applied, a paint of cold galvanization spray should be applied, since the weld destroys this coating.
3.1.2. Fabrication process
The coiled steel in reels is then exported to the manufacturers of profiles which can mold them through two different methods. Bending and rolling.
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Press braking is mainly used to manufacture elements with simpler cross-sections (U, Z or L) and is more advantageous for small-scale production and whose lengths do not exceed 6 meters. This consists of using a press consisting of an upper part with a convex shape (in V or U) that compresses the plate against a lower surface in the inverse (concave) shape. Since it is a less industrialized process that requires at least two operators, the production speed does not exceed 60 meters per minute. [10]
Figure 3-2 - Press braking process [21]
Rolling is the process most used in the manufacture of cold formed sections because it is almost 100% automatic, making it more advantageous in the mass production of batches of profiles with the same section. The process consists in passing the steel strip through a machine composed of a series of sequentially placed compressor rollers (6 to 15) and with different spacing and geometries, which fold the plate as it is drawn, being practicable an average production of 30 meters per minute. At the end of the line the pieces are being cut to the desired length up to a maximum of 12 meters.
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Figure 3-3 - Rolling process [8]
In the same process it is still possible to fabricate closed section profiles using a different machine which after the folding steps still applies a weld seam.
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Figure 3-4 - Cold forming a closed cross-section process [8]
3.1.3. Common cross-sections
Figure 3-5 - Most common cross-sections shapes [21]
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The most popular cross-sections are the U-sections and C-sections. Note that the sections C are also referred to as U-sections with stiffeners. These two sections are the main constituents of the load bearing walls, where U-sections are designated as the tracks where the C-section studs are fixed. These C profiles are also frequently used for the construction of beams, whether front-to-front or back-to-back. (Figure 3-6)
Figure 3-6 - Front-to-front and back-to-back built-up cross-sections [18]
On the other hand, more irregular sections, with more reinforced zones, can be used. This have increased cross-sectional strength, as illustrated in the graph of Figure 3-7. This is the case of the sections in Σ and Ω that by their more irregular geometry can be advantageous in certain cases, being that they are usually more used in the execution of floor beams and ceiling mounts since its more easy to choose the desired height of the web and hence the height of the slab.
Figure 3-7 - Evolution of the critical tension with the increase of stiffeners [22]
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Insulation and claddings
3.2.1. Facade claddings
As previously mentioned, it is necessary to choose carefully the claddings in the execution of light steel projects. It is in facade claddings that this aspect gains special prominence, since these can be mere claddings of the structural elements or claddings that really contributes to the structural performance of the building.
3.2.1.1. Structural claddings
Structural claddings are usually boards of a material with physical and geometric characteristics that provide them with an ability to withstand expected loads, acting as braces and providing rigidity to the building. In view of the importance of these claddings, they must be packed, handled and applied with special care. Since they are an integral part of the structure, they are subject to design and must comply with some norms, such as NP EN 300 which establishes the minimum requirements for OSB structural boards. (Erro! A origem da referência não foi encontrada.)
Table 3-1 - Requirements specified in NP EN 300 to consider a OSB board as structural element [6]
NP EN 300 Thickness 11 – 17 mm 18 – 25 mm Service classes 3 Resistance Longitudinal bending 20 N/mm2 18 N/mm2 Transverse bending 10 N/mm2 9 N/mm2 Tension perpendicular to the board surfaces 0,32 N/mm2 0,30 N/mm2 Young Modulus Longitudinal 3500 N/mm2 Transverse 1400 N/mm2 Maximum swelling percentage 24h ≤ 15 %
Usually this is only used on the exterior face of the building, on the walls, floors and roofs being screwed to provide a diaphragm effect (4.4.3), however, they can also be placed on the inside when it is desired to create a surface that allows the attachment of heavy objects on the wall as furniture or decorations. [6] Having said this, the following are some of the main coatings applied to light steel construction.
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Structural Design of a Light Steel Frame Dwelling
1) Cross laminated timber (CLT)
Figure 3-8 – CLT board [30]
One of the oldest materials used as a structural coating is glued laminates, invented in Germany in the twentieth century by Friedrich Otto Hetzer. These are made up of successive lamellas of wood glued to each other, having the same characteristics of wood, but eliminating natural defects of the material. In solid wood the greatest defect lies in the nodes since these are places where important stresses accumulate. However, since the lamellas are placed one above the other, there is a randomness in the dispersion of these nodes, distributing the accumulated stresses through all the board. [11] They have the advantage of being able to stay in view, which provides a feeling of comfort to the user and allied with the pleasant aspect usually lead to buildings of great beauty. However it falls short to other claddings in some other characteristics.[6]
2) Oriented strand boards (OSB)
Figure 3-9 - OSB boards [31]
The OSB - Oriented Strand Board boards are also composed of wood sheets but shorter, in the order of 10 cm, being arranged in layers with direction perpendicular to the previous layer.
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Structural Design of a Light Steel Frame Dwelling
With many advantages at a reduced cost, these are the preferred choice of contractors in Portugal to coat and reinforce the LSF structure. Firstly, they are quite easy to transport, cut and fix through screws, being that they are prepared to withstand harsh weather during the constructive process. They also allow a simple execution of the materials of finish of facades and has great resistant capacity, being able to support heavy objects such as furniture or decorations. [6] Also, good thermal insulation levels are associated with the excellent structural behavior, making an efficient contribution in the design of LSF structures allowing stress dispersion and structural stability, being extremely resistant, especially when requested in its plan. To prove the strength of this material, walls made with this product were shear tested and the conclusions show that this material guarantees a great stability of these walls and endows them with ductility. [11] The EN 300 standard defines the four classes of OSB according to the environment of use, mechanical characteristics and physical properties, these being: OSB / 1 - General purpose signs, including interior decoration and furniture, in dry conditions OSB / 2 - Plates for structural purposes, in dry conditions OSB / 3 - Plates for structural purposes in a humid environment OSB / 4 - Plates for high structural performance in a humid environment For current LSF structures the most commonly used OSB boards are Class 3 because these ensure proper weather behavior both during construction and in service. Finally, the ideology of sustainability is given great importance, as, for example, Kronospan, one of the world leaders in the production of OSB, ensures that the wood used comes from plantations designed for this purpose and is exploited in a management context sustainable forest, taking advantage of the highest possible yield of raw materials. These also take on the commitments of the PEFC - Program for the Endorsement of Forest Certification schemes and FSC® - Forest Stewardship Council®, where they declare to guarantee the lowest environmental impact on soil, air and water, promote recycling as well as accelerate the recycling of wood residues from other products and also handle, use, condition and destroy chemicals in a safe, healthy and environmentally friendly way. [12]
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Structural Design of a Light Steel Frame Dwelling
3) Cement plates (“Viroc”®)
Figure 3-10 - "Viroc" boards [11]
Cement plates or better known in Portugal by the main brand "Viroc" are composite panels consisting of a mixture of wood particles and Portland cement, dried and compressed. These combine the flexibility of the wood with the strength and durability of the cement and can be applied as a cladding both inside and outside, and are mainly applied when greater resistance to impact, fire, noise, humidity and fungi is required. In contrast, they are substantially more expensive than other existing coatings, and more difficult to apply since they are not only heavier but require a larger screwing surface (metal profiles with larger flanges). Finally, because they are more rigid, they are more susceptible to cracking. [13]
3.2.1.2. Non-structural claddings
In contrast to the foregoing, non-structural coatings are all those which due to lack of valences in their mechanical properties do not comply with the applicable standards to be considered as an integral part of the structure. Its main function is to hide the steel frame and to serve as a surface to the finishing (eg paint or tiles) or be the same the finish itself. In addition to OSB boards whose physical characteristics do not meet the minimum requirements to be considered structural, the main interior linings of LSF structures are gypsum boards, better known as "pladur". The board is fabricated from a wet gypsum slurry and poured continuously onto paper, receiving a new layer on the upper surface, forming a sheet of gypsum wrapped in paper, which upon drying is cut to the desired size. Depending on the additives they receive, they can be used in different environments, such as more humid or ones that require higher fire resistance, and can be used on interior walls and false ceilings [14]
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Structural Design of a Light Steel Frame Dwelling
The plates can be screwed directly onto the metal frame or onto a pre-OSB layer. The joints are treated by the application of reinforced slurry with a strip of paper or netting, in the end being sanded and being ready for final painting or for another type of finish such as tiles. [6]
Figure 3-11 – Different kind of gypsum boards [12]
Furthermore, there are still more advanced materials that offer special advantages in terms of thermal, acoustic or fire resistance, these are not their main functions.
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Structural Design of a Light Steel Frame Dwelling
An example of this material is the Isolpro boards being a composite of lightweight concrete, polystyrene granules, sand, water, fiberglass and an interior structure in galvanized steel, performing thermal and
Figure 3-12 - Scheme of Isolpro boards application on a LSF floor [4] acoustic insulation, and that can be used in both interior and exterior walls, floor coverings and facades, being adaptable to any type of construction system and allowing any finishing. [15]
3.2.2. Thermal insulation
Probably the most important component for the user is the comfort of their home regarding its thermal performance. Therefore, the materials used must provide resistance to temperature variations, however it is accepted that the steel has no property as a thermal insulation. This, for an uninformed customer might raise some doubts about its thermal performance, but the truth is that, for the most part, the surface of a wall in LSF does not have any steel, simply being limited to thermal bridges. Usually the profiles used are 1.5 mm thick and are spaced 60 cm, in addition there are still thermal bridges of 1.5 mm near the floor and ceiling due to the thickness of the web of the lower and upper tracks. The remaining area should be covered by about 4 to 6 cm of rock wool, providing that the percentage of the surface of the thermal bridges is a maximum of 0.375%, with 99.625% of the area being properly insulated. [16] Parallel to the insulation guaranteed by rock wool, it is quite common that the facades of buildings are coated with polystyrene (extruded or expanded), either to ensure the waterproofing of the walls, but also to eliminate thermal bridges. In short, especially due to the "light" component of these buildings, the thermal inertia are practically negligible, which is why the effect of HVAC systems is felt much more quickly, since it is not necessary to heat / cool the walls in order to heat / cool the entire volume of the room. Compared to traditional construction, for the same level of comfort, it is needed less power, and therefore increasing energy savings.
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Structural Design of a Light Steel Frame Dwelling
3.2.3. Acoustic insulation
In order to have a good acoustic performance it is necessary to intercalate high density materials with low density materials. As previously mentioned, the walls of an LSF construction are made up of several layers of different materials. On the one hand, the OSB and the plasterboard provide mass to the walls, while, on the other hand, rock wool is very efficient in acoustic insulation thanks to its mineral structure, high damping and also the reduction of resonance effect in the plasterboard. Finally, it should be noted that extruded polystyrene adds resistance to the passage of sounds. The joint action of these materials leads to the fact that the dwellings in LSF have an acoustic behavior quite different from the traditional construction, being that the sound produced in the interior is not absorbed by the walls, but reflected by these, preventing three times more the propagation of the noise than on a brick wall. Lastly, there is the impact sound, which produces a hollow sound, since the sound is transmitted only partially to the other side of the wall. Due to the lower density of the structural elements and coatings, better insulation of percussion sounds is ensured, however, the aerial sounds are more difficult to insulate with a level similar to the first ones. [16]
Connections
In order to match the various materials mentioned above, there are also different types of connections possible and whose selection depends on the material to be joined.
3.3.1. Steel-to-steel connections
There are currently four types of connections possible to solidify steel elements, namely welding, rivets, nails and screws. Welding should be avoided from being applied as it induces very high residual stresses on the thin sheets and may compromise the strength of the structural profiles. Rivets, as they require prior drilling, become a very time-consuming solution to the intended work rate in LSF construction. Nails, when applied by pressure gun, are a faster solution, however their use is not yet widespread in Portugal. Finally, the most widely used connector is the screws, which should be self-drilling, thus ensuring a good work rate. These should have a "Truss" concave head (commonly referred to as a cheese head) and a length that guarantees at least three threads after the last layer to be fixed. Most commonly used screws have a diameter of 4.2mm or 4.8mm, ie # 8 or # 10 screws.
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Structural Design of a Light Steel Frame Dwelling
However, the diameter, quantity and spacing of screws must be properly dimensioned according to the current regulations (EC3-8), as this should never be used less than 4 screws to join profiles, and these should not be spaced less than 13mm from the edge of the profiles or between them. This way, it is always possible to screw it all over the web and flanges, but never on the lip. [16]
Figure 3-13 - Types of screws heads [32]
3.3.2. Cladding to framing connections
In the connections between the steel profiles and the OSB plates, the screw heads should be at least 7mm in diameter and should be embedded in the OSB, so that there are no protrusions that could cause finishing deficiencies. Since OSB boards perform structural functions, these screws should be at least 9mm apart from the edges of the OSB boards and spaced by a maximum value to ensure the safety of the cutting walls from horizontal forces. This design can be done according to the tables proposed by AISI. [17]
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Structural Design of a Light Steel Frame Dwelling
Constructive Method
Terminology
Firstly, in order to properly understand the construction process, it is necessary to know the various characteristic terms of the metal construction, especially the light steel construction. That said, Table 4-1 shows some terms and their names taken from the LSF Structure Design Manual. [16]
Table 4-1 - Main terms used in LSF construction [16]
Designation Definition Bearing wall Wall that supports mainly gravity loads from slabs or roofs. This shouldn’t be changed after construction. Bracings Normally inclined structural element applied between studs to prevent lateral movement and increase the resistance of the structure to horizontal actions (wind and earthquakes). Can additionally provide more attachment points of the diaphragms (plasterboard or OSB) Buckling Profile deformation due to excessive compression (studs) and / or bending (beams). Buckling in the studs may occur by flexion or flexion-torsion. In beams, buckling may occur by lateral deformation (lateral buckling). In both cases (studs and beams) local buckling may still occur (deformation of the sections without deformation of the structural element axis). C-section Cold formed cross-section with the shape of an “C”, composed by one web, two flanges and two stiffeners. This profile is used to support mainly axial loads (studs). The dimensions of the cross-section are measured by the exterior. Clip Piece that allows the connection between orthogonal profiles. This piece must always be of thickness equal to or greater (whenever possible) to the profiles to be connected. As a rule, clips are in the form of a short angle section with the same flange or (less common) a short section with a U or C section are used. Eaves Part of the console roof extending beyond the facade plane
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Structural Design of a Light Steel Frame Dwelling
Flange Section (or wall) of profiles C and U perpendicular to the web, generally 43 mm wide (maximum 50 mm) Gable Exterior walls perpendicular to the façade, usually without windows and without significant loads applied, except for those transmitted by the ridge beam (if any). Interrupted Studs below the sill of a window or above the same, or more frequently, above the stud blinders box, which only purpose is to create points to fixate the diaphragm. Doesn’t have any applied loads. King studs Studs on the sides of the openings that receive loads from that span. These studs don’t overcome all the height so they must be fixed to other studs that do overcome all the height. Lintel Beam (C-profile or truss) above a door or window span. Lip Also known as stiffeners, it is each part of the plate parallel to the web on the open side of a C-profile which makes the flanges stiffer and the cross-section more symmetrical, reducing the distance between the geometric center and the shear center. This allows to increase the resistance of the section to bending and also to local instabilities. Partition wall Wall whose only function is to create divisions. No significant loads are applied. Their disposition com be easily changed. Ported The “philosophy” of construction underlying the LSF; alignment, as far as Alignment possible, of the sturdy elements of the construction, to transmit the loads to the ground by pure compression on these elements. In vertical elements, the generated moments are negligible. This philosophy deals with the concept of load distributed (albeit only in the “knife load” version (kN / m) as opposed to the logic of the typical concrete pillar-and-beam construction where point loads are generated). Ridge Horizontal edge at the meeting of two waters Shear wall Wall designed to face loads applied on its own plan (horizontal loads), general rule with resistant diaphragms and/or diagonal bracings. Span Distance between two supports of an horizontal element Strip Metal sheet without any folds of a given width. These elements can only be subjected to tension, so they are usually used in pairs. (In a panel under shear loads, one of the diagonals is subjected to tension an the other to compression). In general, panels have diaphragms that dismiss the use of these strips, so they are only used when these panel receive loads before the fixation of this diaphragms. (for example, in interior walls where the claddings are only applied when all the structure is finished.) Structural The panels claddings when they are effectively working as a diaphragm. Usually claddings in OSB but can be with others board materials. Gypsum when used with only one layer has no structural resistance. Studs Vertical structural element that receives loads from beams and transfers them to the inferior floor, overcoming all the floor height.
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Structural Design of a Light Steel Frame Dwelling
Tracks (upper U-profiles where the studs are fixed at floor and ceiling level. At ground level and lower) (foundation slab) they are normally fixed on asphalt screen with chemical bushing. Truss Structure formed by bars and nodes in which the nodes rotations are allowed. The loads must be applied on these nodes and so the only stresses on the bars are axial tension or compression. U-section Cold formed cross-section with the shape of an “U”, composed by one web and two flanges. These profiles are made to support mainly shear loads (beams), or for constructive reasons (tracks). The dimensions of the cross-section is measured by the interior. Web crippling Plastic deformation (irreversible) of the web due to the action of excessive concentrated local loads or due to support reactions.
Foundations
The foundations of an LSF building is basically the same as in any other traditional construction since they are still made of reinforced concrete elements. However, it is more often used lintel beams around the building, as well as the remaining interior walls that receive load. On the other hand, it is also very common to use ground slabs, since it’s a method that requires much less time consuming. Note that, generally, the foundations of steel structures are smaller, since the permanent loads are also smaller than those found in concrete or masonry construction. Having this said, the foundations must be designed to resist the vertical forces as well as the uplifting induced by the wind forces. However, these are always limited to a minimum of 20 cm, as the lower tracks are fixed to foundations through various M16 bolts, spaced 50 cm apart, and fixated using chemical bushing.
Figure 4-1 - Scheme of track to foundation connection [19]
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Structural Design of a Light Steel Frame Dwelling
That said, as these are elements in reinforced concrete, they are no longer dealt with further detail in this dissertation.
Constructive methods
According to experience of the constructor, the kind of building and the required fastness, there are essentially four light steel construction methods, which can be defined as follows:
4.3.1. Stick construction
In this construction method, discrete members are assembled on site to form columns, walls, joists, beams or braces, to which the cladding, interior linings and other elements are affixed. The profiles usually come from the factory pre-cutted with exact dimensions as well as with open holes for the passage of the installations, however, the connections are made in situ using self-tapping and self- tapping screws. The main advantages of this method are: Any modifications can be accommodated on site, as well as ensuring the tolerances of the construction. Relatively simple construction technique. The contractor is not required to have a prefab factory as in panel construction or modular. Large quantities of structural elements can be accommodated and transported in single loads. Element construction usually requires a lot of labor on the construction site, however it can be very useful when dealing with more complex constructions where prefabrication is not a viable solution. [18]
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Structural Design of a Light Steel Frame Dwelling
Figure 4-2 - Stick construction [19]
4.3.2. Panel construction
In order to reduce construction time on site, wall and floor panels, as well as roof trusses can be prefabricated on factory and then assembled on site. Considering that these elements are built in the factory, better accuracy is more easily achieved by mitigating possible deficiencies that could be noticed in the finishes.
Therefore, the main advantages of this method are: Building erection speed. Quality control in production. Minimization of costs on site. Possible factory production automation. Because panels are prefabricated in a controlled environment, the geometric accuracy and reliability of these and other components is enhanced. Good preparation for quick assembly of the panels is essential in order to obtain a good efficiency of the construction process on site. Finally, the size and weight of the panels are determined by transport service, erection facility and on- site assembly. [18]
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Structural Design of a Light Steel Frame Dwelling
Figure 4-3 - Panel construction [19]
4.3.3. Modular construction
In modular construction, the so-called volumetric units are completely prefabricated on factory and can be delivered on site with all internal trim, fixtures and fittings properly installed. The units are placed side by side or stacked on top of each other to be assembled in their final form. Alternatively, these modules can be inserted into buildings already constructed to create pre-built partitions. This type of construction has been gaining in popularity especially in the case of mass construction due to economies of scale, quality control and rapid on-site construction. [18]
Figure 4-4 - Modular construction [19]
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Structural Design of a Light Steel Frame Dwelling
4.3.4. Balloon frame construction
This method is in fact a complement to the methods of elemental construction or panel construction, since in platform construction the walls and floors are constructed sequentially, one floor at a time, and the walls are not structurally continuous. In some forms of construction, loads from the upper walls are transferred from the floors to the lower walls. That is, in platform construction, the floors rest directly on top of the upper wall rail. This type of construction is mainly used in domestic scale buildings. On the other hand, the "balloon" construction, the wall panels are usually much larger and are also continuous on more than one floor, being the floors fixed to the side of the walls. The loads of the upper walls are transmitted directly to the lower ones. [18]
Figure 4-5 - Platform construction (on the left) and balloon frame construction (on the right) [18]
In both construction cases, the exterior cladding and finishes are installed and affixed to the profiles on site. Bracings
All structures must be of adequate stiffness to prevent excessive displacements when required by horizontal forces such as wind forces or seismic forces. There are three main ways of ensuring the structure's stability in the vertical plane: “K” integral bracing, X bracing and diaphragm effect action. Either method offers a viable solution for transferring wind forces to foundations.
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Structural Design of a Light Steel Frame Dwelling
4.4.1. K - Bracings
In this method, C-section profiles are fixed diagonally between the vertical uprights within the thickness of the profiles. The diagonal members of the brace should be well fixed to the vertical elements to ensure the transfer of forces both in tension and in compression. [19]
Figure 4-6 - K-Bracings [18]
4.4.2. X - Bracings
X-crossed thin steel sheets are attached to the outer faces of the uprights. These strips act only in tension and can bend unless pre-tensioned during installation. Crossbands must be fixed to all vertical elements. [19]
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Structural Design of a Light Steel Frame Dwelling
Figure 4-7 - X-Bracings [18]
4.4.3. Diaphragm Effect
Both walls, floors and roofs are often covered with boards of suitable materials (eg chipboard, chipboard, or plasterboard) that act as structural diaphragms for transferring forces to braces or foundations. This diaphragm effect is achieved by attaching the structural plates to the metal profiles using self- drilling screws never spaced more than 300mm apart. The diaphragms can also be used in the horizontal plane as the floors must be designed to drive the shear forces to the bracing walls. Note that if there are areas with significant openings (such as windows or doors), it is important to ensure that the force path is maintained. Eurocode 5 proposes a method for detailed diaphragm design which, although directed to wooden structures, its principles can be adopted for light steel structures. [19]
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Structural Design of a Light Steel Frame Dwelling
Design regulations
The design of steel structures made of cold formed profiles is usually characterized by the complexity resulting from the high slenderness of the cross sections. This high slenderness potentially causes cross- sectional distortion phenomena, in addition to the local section and global buckling, traditionally present and regularly treated for hot-rolled sections.
In regulatory terms, and in the context of the Structural Eurocodes development program and in particular EC3 (Design of Metal Structures), this additional complexity has led to the elaboration of a specific part of EC3 to deal with the design of cold formed profiles, to part 1.3. Finally, it will be necessary to use Eurocode 5, relative to wood structures, in order to design and do all the required safety checks on the OSB diaphragms, which guarantee the safety to horizontal loads.
Cold-formed steel specific phenomenon
5.1.1. Local buckling
The high slenderness of the different elements that make up the cross-section leads to local buckling phenomena, which must therefore be explicitly considered in the design of this type of section. In addition, the post bending strength of thin elements is usually stable, so it is possible to consider the post bending reserve when sizing these sections in order to obtain an economical solution.
According to Eurocode 3, part 1.3, the design of cold formed elements is based on the effective section method. This method considers the reduction of section strength due to local buckling by reducing the size of each of the cross-section elements (effective section).
5.1.2. Torsion
The slimness of the cross sections implies a normally very low torsional stiffness. Most sections produced by the cold hanging process are monosymmetric or even asymmetric, and where the shear center does not coincide with the center of gravity of the section, therefore it is essential to consider secondary torsional moments due to the eccentricity between the axis. load action and the shear center. Thus, it may be necessary for such elements to be restricted to torsion either at regular intervals or continuously over their entire length.
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Structural Design of a Light Steel Frame Dwelling
5.1.3. Distortion
Cross sections prevented from laterally deforming and / or twisting may still undergo a buckling mode commonly referred to as distortion buckling. This mode of buckling may occur in compressed and / or flexed limbs. EC3-3 considers the reduction of section strength due to distortion buckling by reducing the thickness of the reinforcement. [20]
Cross-section classifications
As is Known, structural steel profiles cross sections, regardless of being welded or hot rolled, are formed by assembling individual plate elements. This, when in compression, can buckle locally Local buckling in cross sections may limit the load bearing capacity by preventing yield stress from being achieved. Even though the cross-sections of cold formed sections come from a single piece (plate) which has been bent to form the final section, ii is in the end made up of several slender elements. I tis further evident that because it’s walls are so thin, the possibility of this phenomenon is even greater.
According to EC3., cross sections can be classified as the following: Class 1 – Cross sections which can develop plastic hinges, with enough rotation capacity to perform a plastic analysis, without reducing its resistance; Class 2 – Cross sections which can achieve the resistant plastic moment, but which rotation capacity is limited by local buckling; Class 3 – cross sections where the tension in the farthest compressed fiber, calculated using a elastic distribution of stress, can achieve the yielding stress, but where the local buckling can stop the plastic resistant moment from being fulfilled; Class 4 – Cross sections where local buckling occurs before the yielding stress in one or more parts of the cross section. Eurocode 3 also exposes that the class of sections depend on the slenderness of the comprised element (length-thickness ratio), and also on the demand, class of steel, and kind of profile. Through tables 5-1 and 5-2, it’s possible to calculate the parameters identified and whenever a cross section is not in the limits of a class 3 then it will be considered as class 4, and so it is required to considerate buckling calculation. The classes of the web and flanges can be different, but the class of the cross section will be the highest of them all, meaning the worst case.
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Structural Design of a Light Steel Frame Dwelling
Table 5-1 Maximum width-to-thickness ratios for compression parts [21]
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Structural Design of a Light Steel Frame Dwelling
Table 5-2 - Maximum width-to-thickness ratios for compression parts [21]
Effective properties
When the profile is in fact class 4, the effective resistance should be based on the effective cross section. Effective cross sections are equivalent to cross section class 4 but with reduced dimensions, obtained by disregarding the material in the areas susceptible to buckle. With this new effective cross section, the effective properties can be calculated through a linear-elastic calculus. The effective length of the comprised elements is calculated through a reducer factor p, defined as a function of normalized slenderness of the element.
Resistance of cross-sections
In order to ensure safe conditions, the axial force, Ned must meet the following criteria: 푁 ≤ 1.0 푁
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Structural Design of a Light Steel Frame Dwelling
5.4.1. Axial tension
The design resistance of a cross section for uniform tension Nt,Rd should be determined from:
f 퐴 푁 , = 훾
5.4.2. Axial compression
The design resistance of a cross section for compression Nc,Rd should be determined from:
f 퐴 푁 , = 훾
Figure 5-1 Effective cross-section under compression [4]
5.4.3. Bending moment
The design moment resistance of a cross-section for bending about one principal axis Mc,Rd is determined as follows:
W 푓 푀 , = 훾 For biaxial bending the following criterion may be used:
푀 , 푀 + , ≤1 푀 , 푀 ,
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Structural Design of a Light Steel Frame Dwelling
Figure 5-2 - Effective cross-section for bending resistance to bending moments [4]
5.4.4. Shear force
The design shear resistance Vb,Rd should be determined from:
ℎ sinՓ 푡푓 푉 , ≤ 1 훾
The value of the shear strength considering buckling – fbv is according to Table 5-3
Table 5-3 - Shear buckling strength fbv [4]
The relative web slenderness λw should be obtained from the following: For webs without longitudinal stiffeners:
푆 푓 휆 = 0,346 푡 퐸
For webs with longitudinal stiffeners:
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Structural Design of a Light Steel Frame Dwelling
푆 5,34 푓 푆 푓 휆 = 0,346 푏푢푡 휆 ≥ 0,346 푡 푘 퐸 푡 퐸 where:
2,10 훴 퐼 푘 = 5,34+ 푡 푆
Figure 5-3 - Longitudinally stiffened web [4]
5.4.5. Torsional moment
Where loads are applied eccentric to the shear center of the cross-section, the effects of torsion should be taken into account. In cross-sections subjected to torsion, the following conditions should be satisfied:
푓 휎 , ≤ 훾
푓 /√3 휏 , ≤ 훾
푓 휎 , + 3 휏 , ≤ 1,1 훾
5.4.6. Local transverse forces
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Structural Design of a Light Steel Frame Dwelling
To avoid crushing, crippling or buckling in a web subjected to a support reaction or other local transverse force applied through the flange, the transverse force FEd shall satisfy:
퐹 ≤ 푅 ,
For a cross-section with a single web, must satisfy the following criteria: ℎ ≤ 200 푡
푟 ≤6 푡
45°≤Փ ≤90°
Figure 5-4 - Examples of cross-sections with a single web [4]
When the cross-sections satisfy this criteria, the local transverse resistance Rw,Rd may be determined according to the respective case presented on the section 6.1.7.2 of the Eurocode 3-3 [4]. These cases are defined according to the position of the local transverse loads, whether they are single or two opposing local loads, and if the web rotation is prevented. On the other hand, for cross-sections with two or more webs, including sheeting, like in the Figure 5-5, the local resistance of an unstiffened web may be determined according to section 6.1.7.3., attending that the following criteria is fulfilled: ℎ ≤ 200sinՓ 푡
푟 ≤ 10 푡
45°≤Փ ≤90°
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Structural Design of a Light Steel Frame Dwelling
Figure 5-5 - Examples of cross-sections with two or more webs [4]
For elements with two or more webs, the local transverse resistance Rw,Rd per web of cross-section should be determined from: